Donor clusters in silicon. II. ESR simulations

Previously reported ESR studies of P-doped silicon have been analyzed in terms of donor clusters. Simulated spectra based on a Poisson distribution of clusters and a binomial distribution of hyperfine intensity inadequately described the peak heights of the experimental data. In the present report, an alternative approach is taken which simulates the effects due to topological hyperfine and cluster-cluster interactions. A computer-generated system of donors is partitioned into clusters, retaining all interdonor exchange energies greater than some critical Jc. The matrix eigenvalue problem for each cluster is solved numerically and the results used to calculate transition energies and probabilities. Simulated spectra produced in this manner show good quantitative agreement with the data.